# NAG Library Routine Document

## 1Purpose

f06chf applies a complex similarity rotation having real cosine and complex sine to a $2$ by $2$ complex Hermitian matrix.

## 2Specification

Fortran Interface
 Subroutine f06chf ( x, y, z, c, s)
 Real (Kind=nag_wp), Intent (In) :: c Complex (Kind=nag_wp), Intent (In) :: s Complex (Kind=nag_wp), Intent (Inout) :: x, y, z
#include nagmk26.h
 void f06chf_ ( Complex *x, Complex *y, Complex *z, const double *c, const Complex *s)

## 3Description

f06chf applies a complex similarity rotation, with parameters $c$ (real) and $s$ (complex), to a given $2$ by $2$ complex Hermitian matrix; that is, it performs the operation:
 $x y y- z ← c s- -s c x y y- z c -s- s c ,$
where $x$ and $z$ are real.
The argument x and z which hold $x$ and $z$ are declared complex for convenience when using the routine to operate on submatrices of larger Hermitian matrices.
Note that:
 $z y- y x ← c w- -w c z y- y x c -w- w c ,$
where $w=-\stackrel{-}{s}$, so to use f06chf when $y$ is the $\left(2,1\right)$ element of the matrix, you can make the call
```Call f06chf(z, y, x, c, -conjg(s))
```
None.

## 5Arguments

1:     $\mathbf{x}$ – Complex (Kind=nag_wp)Input/Output
On entry: the value $x$, the $\left(1,1\right)$ element of the input matrix.
On exit: the transformed value $x$.
2:     $\mathbf{y}$ – Complex (Kind=nag_wp)Input/Output
On entry: the value $y$, the $\left(1,2\right)$ element of the input matrix.
On exit: the transformed value $y$.
3:     $\mathbf{z}$ – Complex (Kind=nag_wp)Input/Output
On entry: the value $z$, the $\left(2,2\right)$ element of the input matrix.
On exit: the transformed value $z$.
4:     $\mathbf{c}$ – Real (Kind=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
5:     $\mathbf{s}$ – Complex (Kind=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.

## 8Parallelism and Performance

f06chf is not threaded in any implementation.